The study of music is part of biology.
Music exists because people create it, perform it and listen to it. People are living organisms, and biology is the study of living organisms.
Any theory of music that claims to be complete must be able to pass the Luxury Yacht Test.
If you succeeded in developing a complete theory of music, you would be able to use that theory to compose strong original music, which you could then sell, and use the proceeds to purchase a luxury yacht. Be suspicious of anyone claiming to completely understand what music is who does not own a luxury yacht. (And no, I do not own a luxury yacht. It follows that the theory revealed in my book is not complete. I claim only that it is plausible and that it explains more about music than anyone else's theories.)
The human brain is an information processing system.
An information processing system has four basic components: input, output, calculation and storage. Applying this framework to the analysis of music, music appears to represent the input. What kind of information is the output, and what does it mean? How is it calculated?
Music is a super-stimulus for the perception of musicality in speech.
Musicality is a perceived attribute of speech, which tells the listener important information about the speaker and the speech. Music is a super-stimulus for this perceived musicality, i.e. music is "speech" that has been contrived to have an unnaturally high level of musicality.
Each aspect of music is a super-stimulus for a corresponding aspect of the perception of musicality of speech.
By investigating each aspect of music, we can make an intelligent guess as to the nature of the cortical map for which the musical aspect is a super-stimulus, and then we can determine what the response of that same cortical map would be to speech, and finally we can determine what role the cortical map plays in the perception of ordinary speech.
"Normal" stimuli for specific aspects of speech perception may lack properties of corresponding musical super-stimuli.
Musical harmony consists of simultaneous pitch values, yet perception of simultaneous pitch values from multiple melodies has no relevance to speech perception (i.e. we almost always only listen to one person speaking at a time). The normal function of the cortical map that responds to consonant relationships between different notes occurring at the same time within harmonies and chords must be the perception of consonant relationships between pitch values occurring at different times within the same speech melody.
Normal speech melody is not constructed from musical notes selected from a musical scale. The normal function of the cortical map that responds to discontinuous musical melodies constructed from musical scales must be the perception of continuous speech melody.
The rhythm of speech is not as regular and structured as the rhythms of music. The normal function of the cortical maps that respond to the regular rhythms of music must be the perception of irregular speech rhythm.
Dance is an aspect of music.
In other words, dance is not just something which accompanies music, dance actually is music. Music is a super-stimulus for aspects of speech perception, but speech perception is not just the perception of sounds: it also includes perception of the speaker's movements such as facial expressions, body language and hand gestures. Dance can be identified as the super-stimulus for this component of speech perception.
There are at least five and possibly six symmetries of music.
These are:
Pitch translation invariance
Time translation invariance
Time scaling invariance
Amplitude scaling invariance
Octave translation invariance
Pitch reflection invariance
Each of these symmetries represents an invariance of some aspect of the perceived quality of music under the corresponding set of transformations.
For each symmetry we can ask "Why?" and "How?".
The first four symmetries are functional symmetries in that they satisfy a requirement for invariance of perception, i.e. for each symmetry in this group our perception of speech should be invariant under the set of transformations that define the symmetry. For example, perception of speech melody is invariant under pitch translation so that people with different frequency ranges can speak the same speech melodies, and have those melodies perceived as being the same. The last two are implementation symmetries which play an internal role in the perception of music. (For example see the next item on octave translation invariance.)
In some cases the "how" part of the question has an answer less trivial than one might assume at first. It turns out that we can identify components of speech perception from hypotheses about the existence cortical maps that respond to aspects of music, and these components reflect the need to achieve perception of speech melody invariant under pitch translation and time scaling.
Octave translation invariance is an implementation symmetry which facilitates the efficient subtraction of pitch values.
Octave translation invariance is the result of splitting the representation of pitch into a precise value modulo octaves and an imprecise absolute value. This split enables the more efficient representation and processing of pitch values, particularly when one pitch value must be "subtracted" from another to calculate interval size.
Our perception of relative pitch must be calibrated somehow.
This explains the importance of consonant intervals in music perception. Consonant intervals correspond to the intervals between the harmonic components of voiced sounds in human speech, and they provide a natural standard for calibrating the comparison of pitch intervals between different pairs of pitch values. Our accurate ability to calculate and compare pitch intervals enables the pitch translation invariant perception of speech melody.
Musicality corresponds to the occurrence of constant activity patterns in cortical maps.
The regularities of time, pitch and repetition in music cause the cortical maps responding to music to become divided up into active and inactive zones, where the division remains constant for all or part of a tune.
Constant activity patterns in the speaker's brain are echoed by similar constant activity patterns in the listener's brain.
Occurrence of constant activity patterns in the speaker's brain represents information about the internal mental state of the speaker. One consequence of the perception by the listener of constant activity patterns in the speaker's brain is a reinforcement of the listener's emotional reaction to what the speaker is saying. This accounts for the emotional effect of music.
Music Theory
In the case of music, there is a substantial descriptive theory of music, which corresponds to a large degree to what is called "music theory", which is almost like a scientific theory, but not quite. Anyone who learns to play an instrument or learns to read music notation will learn some of this descriptive theory. It includes concepts like frequency and tempo, and all the components of music such as melody, scales, chords and rhythm.
Although music theory tells us something about what music is, there is still quite a lot that it doesn't tell us:
Firstly, music theory is not complete. Music theory defines what is effectively a set of constraints on what music can be, for example the constraint that pitch values in a melody come from a finite set of values in a musical scale. But the set of constraints is not complete, and to further complicate things, some constraints only seem to apply to some kinds of music. This incompleteness implies that music theory is not fully predictive, in the sense that it cannot completely predict the musicality or "strength" of an item of music from its description. Because music theorists do not traditionally think of themselves as doing scientific theory, the incompleteness of music theory is often regarded as some kind of ineffable mystery which is intrinsic to the very nature of music. This type of anti-scientific mysterianism is of course a general feature of how people think about mental phenomena in general, like the existence of the human "soul", so most people have little difficulty accepting that it should also apply to music.
Secondly, music theory does not say anything at all about what is going on inside the human brain when we listen to music. What goes on inside the human brain (or any brain for that matter) is quite mysterious anyway, so it should perhaps not surprise us that what goes on inside the human brain when we listen to music is mysterious. But because music does not have any existence independently of its human perception, we cannot consider any theory of music to be complete until it does explain the detailed mechanics of how our brains respond to music. This is different to, say, temperature, where we can understand what "hot" and "cold" are, even if we don't understand the physiology of the perception of hot and cold.
Thirdly, and finally, music theory does not say anything about what music is for. If you asked most people why they listened to music, they would probably answer that they listen to it because they like it. This doesn't really explain anything, because most things we do because we like them, or because they have some relationship to getting something that we like. The real question is why do we like music, and our ignorance of the answer to this question is truly profound. It's not hard to give some kind of explanation of why we like most of the things that we like, and to determine some relationship with survival and successful reproduction. But music doesn't seem to relate in any obvious way to anything else other than music.
There exist certain patterns of sound which people create, which have certain emotional and pleasurable effects on the listener.
These patterns of sound are subject to certain constraints, some of which can be described with some degree of mathematical precision, and these descriptions form the content of "music theory" which is traditionally taught to those learning about musical composition and performance. However, these descriptions do not fully distinguish between what is music and what is not music.
Given the incompleteness of the descriptions of music provided by music theory, and our ignorance about the biological mechanics of the effect that music has on the listener, and our ignorance about why it has an effect on the listener, the only satisfactory definition of music is a subjective definition, which means providing a list of specific examples, and then saying: "music is anything like that".
The brain and the nervous system constitute the body's information processing system. The brain receives input information from the senses (the traditional five plus various internal senses), and its job is to generate output information, mostly in the form of nerve signals which cause particular sets of muscle fibres to contract.
We can recognise, or at least attempt to recognise, sub-systems of the brain which perform specific sub-tasks of the brain's information processing task. For example, there is an identifiable colour processing sub-system, which inputs information about the colours of light received by the retina when perceiving a scene, and which outputs information about the colours of objects perceived in that scene. Its physical location is in a certain part of the occipital cortex, towards the back of the brain. The colour processing sub-system is discussed in detail in Semir Zeki's book A Vision of the Brain.
If music is a major aspect of human mental life, then it seems reasonable to suppose that we could identify a music processing sub-system in the brain. This sub-system would be one that takes in music as its input information, and processes this information to produce some kind of output. But what is the output?
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The most basic perception that comes from listening to music is simply that it is music that we are listening to. When we listen to music we perceive the "musicality" or "musicalness" of the music. The concept of musicalness as a variable quantity reflects the observation that we perceive some music to be more musical (i.e. better, or stronger) than other music.
Another consequence of perceiving music is its emotional effect. However it is generally found that the intensity of the emotional effect of music is proportional to its musicalness, which suggests that the brain calculates musicalness first, and then uses that calculated information to alter its emotional response accordingly. Yet another consequence of perceiving music is pleasure, but the extent of musical pleasure is also a function of musicalness. So we can continue under the assumption that the primary output of the music processing sub-system is musicalness.
But what is the meaning of "musicalness"? If the brain contains a system for calculating the musicalness of music, then the value that it calculates must have some meaning, otherwise why even bother to calculate it?
Does music have any meaning? We can try to answer this question by considering where music comes from. Music comes from those who compose it, and from those who perform it. Why do composers and performers make music? In practice they may have various goals, but it seems likely that, in many cases, particularly with regard to the commercial music that most of us listen to, the main goal is to make music that is as musical as possible.
However, if musicalness is a calculated property of music, and music is just something that has been created to be as musical as possible, then our understanding of the relationship between music and musicalness is too circular.
